The Swedish international confirmed that he will play a practice match within the next few weeks as he looks to regain full fitness.
"Everything feels really good," he said. "I have never been this strong in the leg."
"Then, I will play an Under-21 match the Monday after. I am tremendously keen."
Mjallby confirmed he would like to make the next Old Firm derby on December 7.
"I would like to participate," he said. "But it sounds a bit early and that is a special match where you need to be 100 percent fit.
"But I will do all I can to get ready as soon as possible."
Mjallby admitted he has been frustrated by his current injury problems.
"It has been frustrating," he revealed.
"Last season went so well and then the World Cup, it felt sad when I only got to play a few matches in the autumn."